John Klauder

Lectures on Functional Integration

Given at the University of Florida, Spring Semester 2004.

Functional integration is a tool useful to study general
diffusion processes, quantum mechanics, and quantum field theory,
among other applications. The mathematics of such integrals
can be studied largely independently of specific applications,
and this approach minimizes the prerequisites needed to follow
the material. Although some knowledge of quantum mechanics
would prove useful, the material is presented so that most
of what is needed is included. The course is designed for a
physics audience, with an occasional excursion into material
and style of presentation that is more mathematical than a typical
physics course might present.

Broadly speaking, topics covered include integration, random variables,
stochastic processes, Wiener measure, Feynman path integrals
in various forms, a brief survey of scalar quantum field theory, and
concludes with the presentation of a soluble mathematical model
of a nonrenormalizable quantum field theory that illustrate
efforts that currently represent the frontier of research.

Thanks to Khandker Muttalib whose lecture notes appear here.

Audio & image files copyright John Klauder and the University of Florida.